A coil of resistance $400\Omega$ is placed in a magnetic field. If the magnetic flux $\phi\;( ext{Wb})$ linke

Question

A coil of resistance $400\Omega$ is placed in a magnetic field. If the magnetic flux $\phi\;(	ext{Wb})$ linked with the coil varies with time $t\;(	ext{sec})$ as $\phi=50t^2+4$. The current in the coil at $t=2	ext{s}$ is:

Accepted Answer

According to Faraday's Law of Induction, the magnitude of the induced electromotive force ($|\varepsilon|$) is equal to the rate of change of magnetic flux ($\phi$) .

1.  **Calculate Induced EMF ($|\varepsilon|$):**
    $$ |\varepsilon| = \left| \frac{d\phi}{dt} ight| $$
    Given $\phi = 50t^2 + 4$, differentiating with respect to time $t$:
    $$ \frac{d\phi}{dt} = \frac{d}{dt}(50t^2 + 4) = 100t $$
    At $t = 2	ext{s}$:
    $$ |\varepsilon| = 100(2) = 200 	ext{ V} $$

2.  **Calculate Induced Current ($I$):**
    Using Ohm's Law ($I = \frac{V}{R}$), where $V = |\varepsilon|$ and $R$ is the resistance :
    $$ I = \frac{|\varepsilon|}{R} = \frac{200 	ext{ V}}{400 \Omega} $$
    $$ I = 0.5 	ext{ A} $$

Step-by-Step Solution

Practice All PHYSICS Questions